The authors use Markowitz mean–variance analysis to develop a portfolio performance measure to study the size effect in the UK stock market. Their measure connects the return on the efficient frontier with the actual return on a portfolio for a given risk. It does not require a beta estimate or the use of a risk-free rate but specifies standard deviation as the measure of risk. The authors present evidence that the size effect is present over the entire period of study, 1985–2012.

This research should be of interest to portfolio managers and fund-of-funds managers who construct portfolios to take advantage of the outperformance of small-cap stocks. The size effect has become somewhat controversial with respect to the UK market. Recently, some researchers have shown that the size effect has reversed in the UK market, with small-cap portfolios no longer exhibiting higher returns. The authors provide evidence to the contrary.

They offer further insight into the significance of the size effect, revealing the limitations of the capital asset pricing model (CAPM) and the Fama–French three-factor model with respect to pricing risky assets. Because CAPM beta estimates require well-diversified portfolios, more concentrated and smaller-capitalization portfolios may be better evaluated using standard deviation, which measures both systematic and idiosyncratic risk, as the risk measure. The authors develop an efficient frontier alternative to the CAPM to test for size premiums.

The authors use Datastream to collect monthly stock data for all companies listed on the FTSE All-Share index from January 1985 to June 2012 to test for the size effect. They use only the 204 continually existing stocks available for the time period in their research. These 204 stocks are sorted into five portfolios of at least 40 stocks each. The return on the smallest is then compared with that of each of the larger portfolios.

Then, they form size portfolios of stocks at the beginning of 2000. For this time period, 413 stocks existed continually. The authors sort the 413 stocks into 10 portfolios of at least 40 stocks each and, once again, the return on the smallest is compared with that of each of the other portfolios.

The authors develop a performance measure (Markowitz deficit, or MD measure) for the size portfolios that takes into account the difference between the return for a given risk on the efficient frontier and the actual return. The MD measure shows the amount of return that can be achieved when the portfolio is efficient. Portfolios closer to the efficient frontier have a lower MD and better performance because reducing the MD approaches the theoretical maximum return for each level of risk.

According to the authors, idiosyncratic risk is negatively related to portfolio size. Also, it cannot be diversified away without incurring cost, which becomes more expensive for small portfolios. The authors’ findings suggest that there is a relationship between idiosyncratic risk and abnormal return. Better-diversified and larger-cap portfolios have less idiosyncratic risk. The idiosyncratic risk of smaller-cap portfolios comprises between 31% and 44% of total risk, whereas the largest-cap portfolios have less than 10% idiosyncratic risk. Historically, smaller stocks have outperformed larger stocks, perhaps because of their higher level of idiosyncratic risk.

Survivorship bias is addressed by including four subperiods for reporting the size effect to increase the sample size. Over the full sample period, the smallest stocks outperformed the largest stocks by approximately 50 bps per month. Estimates of survivorship bias range from 3.7% to 4.5% per year.

The authors perform extensive literature searches and mention many prior studies that have conclusions contradictory to their own. Although these prior researchers used different time periods and markets, survivorship bias can greatly influence results and might be a factor in the contradictory results. Because the authors focus solely on UK markets, I would be interested in more data about the effect of survivorship bias on the performance of the FTSE All-Share Index. For example, the inclusion of tables showing the frequency of and reasons behind various stocks dropping out of (because of bankruptcies, mergers, buyouts, and so forth) the FTSE All-Share Index during the various time periods studied would be helpful.